Solve for $x$ and $y$ using elimination. ${4x-2y = 28}$ ${-5x+3y = -34}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $2$ ${12x-6y = 84}$ $-10x+6y = -68$ Add the top and bottom equations together. $2x = 16$ $\dfrac{2x}{{2}} = \dfrac{16}{{2}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {4x-2y = 28}\thinspace$ to find $y$ ${4}{(8)}{ - 2y = 28}$ $32-2y = 28$ $32{-32} - 2y = 28{-32}$ $-2y = -4$ $\dfrac{-2y}{{-2}} = \dfrac{-4}{{-2}}$ ${y = 2}$ You can also plug ${x = 8}$ into $\thinspace {-5x+3y = -34}\thinspace$ and get the same answer for $y$ : ${-5}{(8)}{ + 3y = -34}$ ${y = 2}$